UHECR Source Identification via Black Hole Parameters: Distance Formula, Dark Black Holes, the Amaterasu Particle, and Primordial Black Hole Dark Matter

This collection contains+fourtpreprints on ultra-high-energy cosmic ray (UHECR) source identification using black hole parameters: Paper I: "An Analytical Distance Formula for Ultra-High-Energy Cosmic Ray Sources" Closed-form formula connecting observed UHECR energy to source black hole parameters (mass, spin, magnetic field) through GZK energy loss. Validated against M87, Centaurus A, NGC 1068, Markarian 501, and the TA Hotspot (4/5 consistent). Introduces critical BH mass M_crit separating neutrino-dominated from UHECR-capable sources. [v2: corrected M_crit numerical value and NGC 1068 iron calculation] Paper II: "Dark Black Holes: UHECR Backtracking as a New Observational Channel" Novel method for discovering electromagnetically invisible supermassive black holes using UHECR backtracking. Four candidate locations identified at 21-82 million light-years. Highest-confidence candidate in Ursa Major (TA Hotspot, 5.1 sigma). Paper III: "The Amaterasu Particle and Precessing Black Holes at the Edge of the Local Void" Precessing, quiescent SMBH model for the 244 EeV Amaterasu particle. Source constrained to d = 10-17 Mpc with M >= 1.1e9 M_sun. Predicted source constellation: Hercules (protons), Ophiuchus (CNO), or Aquila (iron). Paper IV: "Dark Black Holes as Probes of Primordial Black Hole Dark Matter" [NEW] Connects UHECR dark BH discovery to primordial black hole (PBH) dark matter. Proposes galaxy-by-galaxy correlation test using M_BH-M_halo relation and a rotation curve-UHECR correlation test. Preliminary analysis with SPARC catalog and Auger/TA data yields null result (insufficient statistics). Estimates TA x4/GRAND can constrain f_PBH to 1e-5 in the supermassive range.